Molei Tao (GaTech)
Numerical methods for identifying hyperbolic periodic orbits and characterizing rare events in nongradient systems
We consider differential equations perturbed by small noises. The goal is to quantify what noises can do and possibly also utilize them. More specifically, noise-induced dynamics are understood by maximizing transition probability characterized by Freidlin-Wentzell large deviation theory. In gradient systems (i.e., reversible thermodynamics), metastable transitions were known to cross separatrices at saddle points. We investigate nongradient systems (which may no longer be reversible), and show a very different type of transitions that cross hyperbolic periodic orbits. Numerical tools for both identifying such periodic orbits and computing transition paths are described. If time permits, I will also discuss how these results may help design control strategies.